Systems and methods for random-access power management using packetization

ABSTRACT

Systems and methods for distributing electric energy in discrete power packets of finite duration are presented. Systems may include an aggregator for providing power packets to one or more nodes. An aggregator may receive requests for power packets from nodes. In other embodiments, an aggregator may transmit status broadcasts and nodes may receive power packets based on the status broadcasts.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a U.S. national stage patent application under 35U.S.C. 371 of PCT/US2014/019719, filed on Mar. 1, 2044, which in turnclaims priority to U.S. Provisional Application No. 61/772,533, filed onMar. 4, 2013, the disclosures of each of which are incorporated hereinby reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This disclosure was made with government support under award no. TRC039awarded by the United States Department of Transportation. Thegovernment has certain rights in the disclosure.

FIELD OF THE DISCLOSURE

The disclosure relates to the equitable allocation of a supply ofelectricity to a number of loads.

BACKGROUND OF THE DISCLOSURE

Plug-in hybrid electric vehicles (“PHEVs”) and pure battery electricvehicles (as a group plug-in electric vehicles, PEVs) promise tofacilitate a transportation future that is less dependent on liquidfossil fuels. However, as PEV market penetration increases, vehiclecharging could strain aging power delivery infrastructure. A number ofrecent papers have shown that increases in PEV charging could havedetrimental impacts on medium and low voltage distributioninfrastructure, particularly where PEV adoption is highly clustered.With mass-produced PEVs coming to market and a range of chargingstandards (AC Levels 1-3) established, it is increasingly important tounderstand and mitigate negative impacts that PEV charging might have ondistribution system components, such as underground cables andtransformers.

Some charging of PEVs is envisioned to occur at workplaces, shoppingcenters, etc., where the power distribution is already sufficient tosupport commercial endeavors. However, it is more likely that PEVcharging will primarily occur at a person's home where the existingpower distribution system has been designed for residential scaleservice, which is typically limited by 15-25 kVA transformers andunderground cables that have capacities on the order of 100 kVA. AtLevel-1 charging rates (˜1.4 kW), electric vehicle charging can doublethe electricity use of an average U.S. residence (from 1.2 kW to 2.6kW). At Level-2 charging rates (˜7 kW), residential loads increase evenmore dramatically. This additional load can have substantial detrimentaleffects on residential distribution infrastructure, particularlytransformers and underground cables, even under moderate PEV penetrationscenarios. For example, transformers, substations, and undergroundcables can age rapidly if operated beyond their specified thermal limitsdue to the additional power draw by large loads.

Implementing effective charge management (CM, also known as smartcharging) methods is one step to facilitate the smooth integration ofPEVs. Several previous studies show that with effective CM schemes it ispossible to support large numbers of electric vehicles even withconstrained electric power infrastructure. In many cases it is alsopossible for PEVs to not only avoid negative impacts on the power grid,but also to provide grid services, through Vehicle-to-Grid (V2G)technology.

The CM and V2G control schemes that have been proposed in theliterature, or in industry, generally fall into one or both of thefollowing categories:

1. Centralized optimization or control methods in which each vehiclesubmits information to a central authority, which in turn solves anoptimization problem that produces a charging schedule for each vehicle.

2. Decentralized methods, in which either utilities set a pricing scheme(e.g., a fixed time-of-use price) and vehicles self-schedule based onthose prices, or a market-based scheme is used to generate prices towhich vehicle charge management devices respond.

These two approaches have a variety of advantages and disadvantages.

Centralized schemes have the advantage that they can, under someconditions, produce economically optimal outcomes by minimizing costsand avoiding constraint violations in the distribution system. However,optimization/control methods require that vehicle owners provideinformation (e.g., willingness to pay or anticipated departure times) toa central authority and require that the vehicle owner give up at leastsome autonomy over the charging of their PEV. While the load servingentity would likely compensate the vehicle owner for this loss ofcontrol with a reduced rate for electric energy, this loss of autonomycould be an impediment to adoption of CM schemes. In addition, vehicleowners are unlikely to know in advance their exact travel schedule,which complicates the problem.

The use of dynamic pricing schemes has been suggested to mitigate thedetrimental effects of PEV charging. However, in order for a dynamicpricing scheme to mitigate localized transformer or cable overloading,utilities must install infrastructure that:

(1) determines current capacity and demand; (2) adapts local rates basedon this capacity and demand; and (3) relays this rate information toeach customer. Furthermore, price-based schemes will require a consumercharging system that: (1) can communicate with the power distributionsystem; and (2) enables customers to choose to charge based onfluctuating prices or at least have technology installed for makingcharging decisions. Note that a price-based approach typically requiresthe power distribution system to know specific information aboutspecific customers, which exacerbates existing concerns about dataprivacy and security in a Smart Grid environment.

Simple time-of-use pricing schemes, such as a reduction in rate fornighttime charging, do not have these disadvantages as owners haveflexibility in choosing how they will respond to the change in prices.However, very simple price-based schemes are unlikely to produce optimaloutcomes in terms of avoiding overloads in the distribution network, orminimizing costs. In fact, such time-differentiated pricing couldproduce new load peaks that increase, rather than decrease aging in thedistribution infrastructure.

The stochastic nature of charging behavior is particularly important tohighlight. PEV arrival and departure times vary substantially betweenowners, days, and within days. Feeder load variability and uncertaintywill grow even further with an increase in distributed renewablegeneration. Vehicle CM schemes that do not adapt well to suchuncertainty are unlikely to be successful.

Additionally, other large loads, such as, for example, air conditioningsystems, tax the power distribution grid in similar fashion.Accordingly, there is a need for a charge management scheme thatenhances the equitable distribution of power to customers, improves theoptimal use of the available supply of power, and offers better privacyto customers.

BRIEF SUMMARY OF THE DISCLOSURE

Given the above-described variability in system capacity and in customerloads, the present disclosure is directed to systems and methods with acharge management approach that is simple, yet robust to randomness andthat has substantial advantages over previous approaches which requiresignificant infrastructure upgrades and expose privacy and securityconcerns. The disclosed systems and methods are advantageous in thatthey can be easily adapted to reduce the bandwidth required forcommunications between the power grid and electric vehicles. This maymake smart-charging more feasibly within the context of low bandwidthand high-latency communications systems that are common in currentadvanced metering infrastructure (“AMI”) systems.

The present disclosure treats PEV charging as a random access problemwhere charge is delivered through many ‘charge-packets.’ A charge packet(or “power packet”) is a quantity of electric energy delivered at a rate(power) over a finite period of time (e.g., 1 kWh delivered at 6 kW over10 minutes). The packetization of charge allows distribution systemobjectives (i.e., efficient use of available resources withoutoverloading) and customer objectives (reducing travel costs) to beachieved simultaneously. Leveraging this approach, the presentdisclosure presents an exemplary decentralized charge managementstrategy, which preserves customers' privacy more than many existingcharge management schemes. Simulations of this method indicate that thecost increase of the charge-packet method over an omniscient centralizedoptimization method (which is untenable in terms of informationrequirements) is only 0.9% to 5.2%. Simulation results also show thatthe introduction of randomness in vehicle charging enables constrainedfeeders in the power distribution infrastructure to be fairly andanonymously shared.

While the present disclosure is described and illustrated throughexamples using plug-in electric vehicles, the methods are not intendedto be limited by such examples. The present disclosure is easily usedfor any type of load or a mix of types of loads (e.g., air conditioners,plug-in vehicles, pool heaters, etc.) As such, the method could easilybe adapted to, for example, reducing overloads due to simultaneousthermal (HVAC or water heating) loads.

DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the nature and objects of the disclosure,reference should be made to the following detailed description taken inconjunction with the accompanying drawings, in which:

FIG. 1 depicts a two-state automaton where P₂ corresponds to a higherprobability of PEV charge request and P₁ a lower;

FIG. 2 is a graph showing the distribution of charging window durationsfor PEVs plugging in between 1700 hours and 0800 hours;

FIG. 3A is a graph showing the capacity (solid) and load (dashed) of anexemplary system;

FIG. 3B depicts the charge activity of the exemplary system over the15-hour window by PEV ID;

FIG. 3C depicts the charging completed by each PEV (x-axis) during the15-hour window;

FIG. 4 depicts the ability of another embodiment of the presentdisclosure to democratically allocate charging resources to 100 PEVswhen the power system capacity profile of FIG. 3A is scaled by 75% and50%;

FIG. 5 shows the state probabilities for 100 PEVs with decreasingcharging needs ranging from 100% to 50% charging in an embodiment of thepresent disclosure;

FIG. 6A is a graph of the capacity (solid) and load (dashed) of anotherexemplary embodiment of the present disclosure;

FIG. 6B depicts the charge activity of the embodiment of FIG. 6A overthe 15-hour window by PEV ID;

FIG. 6C depicts the charging completed by each PEV over the 15-hourwindow in the embodiment of FIGS. 6A and 6B, where the required chargesof the PEVs varied (note that each PEV was completely charged during thewindow);

FIG. 7 depicts a three-state (N=3) automaton where P₂ corresponds to alower probability of PEV charge request than P₁, and P₃ to a lowerprobability than P2 (in case of charge urgency (urg=1) the state machinewill stay at P₁, but if there is no charge urgency by driver's call(urg=0), and the power transformer was congested (cong=1), i.e., acharge request was denied to avoid transformer overload, the PEV statemachine will go to a state with lower probability. If charge urgency wasset by the driver (urg=1) the state machine will go to P₁ with thehighest probability);

FIG. 8A is a graph of the load curve of another embodiment, showing theresidential and the aggregate transformer load;

FIG. 8B depicts the PEV status of the embodiment of FIG. 8A, with grayshades indicating: A: PEV is away, HN: PEV is at home but not requestingfor charge (either the battery is full, or it is during peak hours), HM:PEV requested a charge packet, but was denied to avoid transformeroverload (charge mitigation), HC: PEV is at home and charging;

FIG. 8C depicts the PEV automaton state number with the gray shadesshowing each automaton's state at the end of the epoch for theembodiment of FIGS. 8A-8B;

FIG. 9A is a graph showing the load curve of a simple charging methodexample;

FIG. 9B depicts PEV status over time for the simple charging methodexample of FIG. 9A (using the same gray-scale codes as in FIG. 8B);

FIG. 10A is a graph showing the load curve of an optimal chargemanagement example;

FIG. 10B depicts PEV status over time for the optimal charge managementexample of FIG. 10A where the gray levels show the amount of energygiven to each PEV at each hour (in the grey-level bar, “A” shows thetime when the PEV is away; and when at home, hourly charge quantitiesvary between 0 and 4.64 kWh, which is the maximum quantity delivered inthis example);

FIG. 11 is a graph depicting a daily load curve showing base load andthe aggregate load when utilizing different charging methods forcomparison;

FIG. 12A-12D are graphs showing the average total travel costs in 100Monte Carlo simulations, showing gasoline, peak and off-peak electricitycosts separately in four case studies with different PEV penetrationsand battery capacities (bars show the average and black lines show 10thto 50th and 50th to 90th percentile);

FIG. 13 is a set of graphs comparing simple charging and variations inthe present charge-packet method, wherein the top graph shows theaverage total costs over 100 Monte Carlo simulations separatinggasoline, peak, and off-peak electricity, the middle graph shows how theresources are equally accessible to the consumers, and the bottom graphcompares the communication burden for different methods assuming therequesting design approach of the charge-packet method (t₁ and t₂ int₁/t₂ show the request interval and the packet length respectively;different state machines are defined with these state probabilities:SM₁: {P₁=1, P₂=0.5}, SM₂: {P₁=1, P₂=0.5, P₃=0.25}, SM₃: {P₁=0.8,P₂=0.4}, SM₄: {P₁=0.8, P₂=0.4, P₃=0.2});

FIG. 14 depicts a three-state automaton of another embodiment of thepresent disclosure where p is the probability of charge request duringan epoch and is proportional to the ‘urgency’ set by the PEV owner(solid lines indicate state changes when automaton is ‘rewarded’; dottedlines are state changes associated with ‘punishments’);

FIG. 15 is a graph showing the capacity of exemplary distribution systemsimulation in terms of percentage of 100 PEVs charging over thesimulated 10-hour charge window;

FIG. 16A depicts the charge activity over a 10-hour window by PEV IDusing the automaton of FIG. 14;

FIG. 16B depicts the charging completed by PEV over the 10-hour windowof FIG. 16A;

FIG. 17 depicts a four-state automaton of another embodiment of thepresent disclosure where p corresponds to customer's urgency;

FIG. 18A depicts the charge activity over a 10-hour window by PEV IDusing the automaton of FIG. 17 where PEVs have different ‘urgency’;

FIG. 18B depicts the charging completed by PEV over the 10-hour windowof FIG. 18A;

FIG. 19 depicts a four-state automaton of another embodiment of thepresent disclosure;

FIG. 20A depicts the charge activity over a 12.5-hour window by PEV IDusing the automaton of FIG. 19;

FIG. 20B depicts the charging completed (up to a full 10-hour charge)during the 12.5-hour window of FIG. 20A by PEV;

FIG. 21 is a diagram of a system according to an embodiment of thepresent disclosure;

FIG. 22 is a flowchart of a method according to an embodiment of thepresent disclosure; and

FIG. 23 is a flowchart of a method according to another embodiment ofthe present disclosure.

DETAILED DESCRIPTION OF THE DISCLOSURE

The present disclosure can be implemented as a method or system formanaging the power supplied to electrical loads (nodes) in a residentialdistribution system in a manner that requires very little centralizedcoordination.

Residential power distribution systems can be viewed as a resource thatis limited due to thermal limits of medium voltage transformers andunderground cables. These resources are used, for example, to chargePEVs, power air conditioners, and to power other large electrical loads.These resources have variable capacity for providing power depending,for example, on other demands on the system. In the example of PEVcharging, the capacity to provide power for PEV charging variesdepending on other loads (e.g., air conditioners and large appliances)and ambient temperatures. In addition, the driving patterns of PEVowners will vary tremendously, from one customer to the next. Thus, thePEV charging problem can be considered as a system where both supply(system capacity) and demand (PEV load) are random.

A system of the present disclosure comprises an aggregator in electricalcommunication with an electrical distribution network. The aggregatormay be configured to receive requests for power packets, determinewhether or not each request may be granted, and respond to the requests.The system may further comprise a plurality of request stations (or“nodes”). Each request station of the plurality of request stations(e.g., PEV charging stations, air conditioners, pool heaters, etc.) isconfigured to request power packets during time intervals (each, anepoch). In some embodiments, each request station comprises an automatondesigned to send a request to the aggregator (either directly or as abroadcast) for a given epoch according to a probability of the automatonmaking a request during that epoch. In some embodiments, the probabilityof a node making a request during any particular epoch may changeaccording to rules (as further defined below). Node epochs may or maynot align with one another. In other words, the start of an epoch for anode may or may not be at the same time as the start of an epoch for adifferent node.

The present disclosure can be embodied as a system 10 for providingelectrical power comprises an aggregator 12 in electrical communicationwith an electrical power source 90 (e.g., the power grid). Theaggregator 12 is configured to provide electrical power from theelectrical power source 90 as a plurality of discrete power packets eachpower packet having a finite duration. In embodiments of the presentdisclosure, the duration of a power packet may be the same or differentfrom the time intervals between charge requests. In some embodiments,the duration of power packets may or may not be the same. In someembodiments, the time intervals may or may not be the same. Forconvenience, the remainder of the disclosure will discuss embodimentswherein the times intervals and charge packet durations are equal.However, such discussion is not intending to be limiting, and the scopeof the disclosure encompasses the alternative time intervals and chargepacket durations.

The system 10 further comprises one or more nodes 20 (sometimes referredto herein as request stations) in communication with the aggregator 12.As mentioned above, nodes 20 may be PEVs (PEV chargers), airconditioners, heaters, or any other large electrical load. Each node 20is configured to request a power packet from the aggregator 12. Forexample, the node 20 may transmit a request for a power packet to theaggregator 12. Embodiments where nodes 20 transmit to the aggregator 12are termed “duplex” embodiments. The aggregator 12 receives each requestfor a power packet from the one or more nodes 20 and determines whetherto grant or deny each request. The aggregator 12 determines to grant ordeny node 20 requests based on (at least) availability of electricalpower from the electrical power source 90. If a request is granted, theaggregator 12 provides a power packet to the node 20 corresponding tothe granted request. It should be noted that the aggregator 12 mayprovide a power packet to a node 20 in any way. For example, theaggregator 12 may provide a power packet by authorizing or otherwiseinstructing a node 20 to use power and the node 20 will utilize powerfrom the power grid. In some embodiments, if the request is denied, theaggregator 12 sends a denial message to the requesting node 20. In otherembodiments, if the request is denied, the aggregator 12 does notprovide a notification to the requesting node 20. At the end of an epoch(i.e., the beginning of the next epoch), each node 20 is configured todetermine whether additional power is required, and send an additionalrequest accordingly.

In an embodiment where aggregator-node communication happens in only onedirection (a “simplex” embodiment), the aggregator 12 sends a periodicbroadcast of its state (either overloaded or not-overloaded). Each node20 is configured to request a power packet by listening for theaggregator 12 broadcast to determine the state of the aggregator 12.When the node 20 determines that the aggregator 12 state is“not-overloaded,” the request is approved and the node 20 obtains power(e.g., connects its electrical load to power) for the duration of apower packet. At the end of the power packet duration, the node 20 mayrequest another power packet by listening for the aggregator 12broadcast. In this way, the aggregator 12 is said to have provided apower packet to the node 20. When the node 20 determines that theaggregator 12 is “overloaded,” the node 20 does not connect to power andwaits for the next epoch. At the next epoch, the node 20 may request apower packet by listening for the aggregator 12 broadcast.

In some embodiments, one or more nodes 20 are configured to request apower packet during an epoch according to a first request probabilityP₁. For example, where P₁=1, the node 20 will request a power packetduring each epoch. The nodes 20 may each have a first state wherein thenodes have the first request probability, and a second state wherein thenodes 20 each have a second request probability, P₂. The first requestprobability may be greater than the second request probability. Thenodes 20 may be configured to change between states based on thegranting/denial of pack requests. For example, a node 20 in the firststate may be configured to remain in the first state if its packetrequest is granted by the aggregator 12, or change to the second stateif the request is denied by the aggregator 12. Also, a node 20 in thesecond state may be configured to remain in the second state if itspacket request is denied by the aggregator 12, or switch to the firststate if the request is granted by the aggregator 12.

In other embodiments, one or mode nodes 20 may have a third state havinga third request probability, P₃, which is less than the secondprobability. One or more of the first, second, or third states may beselectable by way of a priority selector. In this way, a personoperating a node 20 may have the option of selecting a higherprobability state, for example, where there is a higher urgency.

Systems according to embodiments of the present disclosure may furthercomprise one or more sensors 14 in communication with the aggregator 12.The one or more sensors 14 may be configured to provide a signal to theaggregator 12 according to conditions of the electrical distributionnetwork (e.g., current load, temperature of one or more component,ambient temperature, weather conditions, etc.) such that thedetermination of the aggregator 12 whether or not to grant a powerpacket request may be altered based on signal(s) received from the oneor more sensors 14. Similarly, the aggregator 12 may be programmed withdistribution network capacity data for the request determination. Forexample, the aggregator 12 may be programmed with a maximum load allowedon the distribution network and additionally programmed to allow only apredetermined percentage of the maximum load during a predeterminedwindow of time.

Systems according to embodiments of the present disclosure may furthercomprise an upstream aggregator 16 for hierarchical determinations ofpower packet request grants. In such embodiments, the aggregator 12 (oreach aggregator 12 in cases having more than one aggregator) willrequest power from the upstream aggregator 16. These requests for powerfrom the aggregator(s) 12 to the upstream aggregator 16 may be performedsimilar to or different from requests from the nodes 20 to theaggregator 12. For example, the epoch parameters (e.g., length of time)may be different.

As described above, some request stations 20 may comprise a selector 22.In some embodiments the selector 22 is configured to allow the user ofthe request stations 20, 22 (the customer) to select between more thanone option. The selector may be used, for example, to select between“urgent” or “standard” need. The request station may comprise one ormore sensors in communication with the request station. For example, asensor may determine the charge level of a PEV and provide suchinformation to the request station. In this example, the request stationmay use the charge level of the PEV to automatically switch between“urgent” and “standard” need. In other embodiments, the sensor may be atemperature sensor, or any other sensor (or combination of sensors)useful for informing an automaton of the request station.

The present disclosure may be embodied as a method 100 for managingelectrical loads on a distribution network comprising the step ofreceiving 103 a request for a power packet, the power packet being asupply of electricity for a finite time interval. The method 100comprises determining 106 whether sufficient capacity exists on thedistribution network to grant the request. The method 100 may includethe step of transmitting 109 a response to the received 103 request,wherein the transmitted 109 response indicates that the request isgranted. In some embodiments, a response may be transmitted 109 whereinthe response indicates that the request is denied. In other embodiments,no response is sent when the received 103 request is denied, and thelack of a response is presumed to be a denial. Either of the received103 request and/or the transmitted 109 response may be sent as abroadcast or a private communication between devices of the distributionnetwork. When a request is granted, a power packet is provided 112 tothe requesting device. As previously stated, the power packet may beprovided 112 as, for example, an authorization for the requesting deviceto obtain power.

The present disclosure may be embodied as method 200 for requestingpower from a distribution network comprising the step of determining 203the current request state of a node. For example, a node may determine203 its own request state. The method 200 for requesting power furthercomprises determining 206 whether or not to request a power packet basedon the determined 203 request state and a request probability that arequest should be sent in the current state. If a request should not besent, waiting a predetermined time (an epoch) and repeating the method200. If a request should be sent, a power packet is requested 209 fromthe distribution network. For example, a power packet may be requested209 by transmitting 212 a request to an aggregator on the distributionnetwork. In another embodiment, a power packet by receiving 215 abroadcast state from an aggregator. The method 200 may comprise waitinga predetermined period of time for the request to be granted. If therequest is granted, then receiving 218 a power packet and repeating themethod. If the request is not granted, then the request state may bechanged 221 to a different state, wherein the changed state has arequest probability which is different than the first requestprobability. The new request probability may be lower than the requestprobability. The method 200 is repeated until the node reaches acompletion state.

The present disclosure may be embodied in an aggregator 12 having asource interface 13 in connection with an electrical distributionnetwork. The source interface 13 is in electrical communication with anelectrical power source 90. The source interface 13 may be configured tobe in communication with one or more nodes 20. In another embodiment,the aggregator 12 has a load interface 15 in communication with one ormore nodes 20. The aggregator is configured to perform the aggregatorprocesses as described above. For example, the aggregator 12 may furthercomprise a processor 17. The processor 17 may be programmed. To receiverequests for power packets from one or more nodes 20, determine whetherto grant or deny each received request, and provide a power packet toeach node according to the corresponding request determination.

The present disclosure may be embodied as a node 20 for requestingelectrical power from an aggregator 12. The node 20 comprises anaggregator interface 21 in electrical communication with the aggregator12. The node 20 also include a state register 24 configured to record arequest state of the node 20. The state register 24 may be of any typeknown in the art, for example, a memory component. The node 20 isconfigured to perform any of the node processes described herein. Forexample, the node 20 may have a node processor 25. The node processor 25may be programmed to retrieve a node (request) state from the stateregister 24; determine, based on a request probability of the nodestate, whether or not to request a power packet; and request a powerpacket from the aggregator 12 according to the request determination.

Further Discussion

While managing the charging of each PEV according to a predeterminedschedule is attractive in the ideal to ensure that the power system'scapacity is utilized fully, it is recognized that both PEV needs and thesystem's capacity are dynamic, random quantities. As such, managing thecharging of each PEV according to a predetermined schedule would requiresignificant coordination and communications. This communication wouldnecessarily involve detailed customer information and thus createpossible security/privacy issues. The present disclosure is directed toan alternative approach for managing PEV charging, based on a network ofcharge-management automatons, one per vehicle. This probabilisticautomaton approach allows local determination of whether or not torequest a charge during any particular time interval (i.e., an “epoch”).The probability of that charge request is dictated by the state of theautomaton. Automatons are managed through a broadcast response by acentralized charge manager (nominally located at the distributionstation).

Fundamental to this approach is that the PEV charging is conducted overmany discrete time intervals. These intervals may be referred to as“power packets” or “charge packets.” The packetized approach ensuresthat all PEVs regularly compete for charging capacity, which isespecially important in order to maintain equal access to all vehiclesunder conditions where the distribution system capacity becomesconstrained. Generally, in embodiments of the present disclosure,automatons request a charge packet.

A probabilistic N-state automaton was developed that illustrated theability to control participation of random autonomous agents over a widerange of control values. A simple embodiment (N=2) of the probabilisticautomaton is shown in FIG. 1. If the node (for example, a PEV, a PEVcharger, an air conditioner, etc.) is in the lower state, it willtransmit during a particular epoch with probability P₁. In the PEVapplication, this “transmission” corresponds to the PEV requesting acharge for a finite length of time (or epoch). If the request issuccessful and therefore rewarded by the end user (e.g., a neighborhoodfeeder), the node will move to the higher state and transmit during thenext epoch with probability P₂>P₁.

If a PEV connects to charge and there is insufficient capacity in thedistribution system to support this charging, then the PEV's requestwill be denied and its automaton will move to a lower state (whichreduces the probability of a request occurring in the subsequent epoch).A charge management agent, notionally located at the distributionsubstation, does not track which PEV is requesting charge or the stateof any particular PEV's automaton. All requests are treated equally andPEVs adjust their state autonomously based only on the feedback providedby the charge manager.

In order to attempt to level the load on the distribution system overthe course of a day, a utility may invoke a tariff structure forelectric vehicle smart charging having different rated for “urgent” and“standard” charging modes. In such an environment, automatons may takeinto account an urgency of the customer (e.g., the vehicle owner). Thepriority of charge is selected by the customer by way of a switch at thecharging station. This information does not need to be transmitted tothe utility, other than for billing purposes (which can be handled atthe customer's meter), thereby reducing privacy concerns.

A significant advantage of the proposed approach is that the powerdistribution system can be blind to the vehicle from which the chargerequests are being made and thus anonymity/privacy of customers ismaintained. The management approach is simply to determine whethercapacity in the systems exists, or not. The individual customers,through their automatons, manage/adjust their behavior accordingly.

Another embodiment of an automaton (N=3) is shown in FIG. 14. In thisembodiment, if the PEV charger is in the highest state (i.e., right-moststate in FIG. 14), it will transmit a charge request during the currentepoch with probability 1. If the request is successful and thereforerewarded by the charge manager, the PEV will be charged for the durationof the packet and the automaton will stay in that highest state andrequest a charge again in following epoch. Alternatively, if there isinsufficient capacity in the distribution system to support additionalcharging, the PEV's request will be denied and its automaton will moveto a lower state (which reduces the probability of a request occurringin the subsequent epoch top).

As a result of this approach, each PEV requests a charge independentlyevery epoch based on the probability associated with its current state(e.g., 1, p, p² for the automaton in FIG. 14). The charge manager doesnot track which PEV is requesting charge or the state of any particularPEV's automaton. All requests are treated equally and PEVs adjust theirstate autonomously based only on the feedback provided by the chargemanager.

Embodiments of automatons can be readily adapted to dynamic retailelectricity tariffs. Notionally, a customer has a certain ‘urgency’ tocomplete a charge over a fixed amount of time. This urgency may be tiedto the price the customer is willing to pay for charging. If thispremise is accepted, then there are two (if not more) ways to leverageit for PEV charge management (or ability of an air conditioner tooperate during the epoch, etc.), under the power packet approach.

In some embodiments, the customer is allowed to set their PEV charger ineither “urgent” or “standard” modes. This could establish a pricethreshold at which charging will no longer be requested. The higher theurgency, the higher is this price threshold. In the design of anautomaton, the current price can influence the state at which theautomation is in. In other embodiments, customers pay for the right torequest a charge. That is, the state of the customer's automatonprobability dictates the price paid for every met charge request. Urgentcustomers may set their automaton probability (in FIG. 14) to p=1knowing that they will be requesting charge more frequently and thus bereceiving power packets more quickly. A less urgent customer may settheir urgency lower (e.g., p=0.5) and on average will request at halfthe rate. Should this customer's request be accepted, the power packetwould be received at a lower cost than for the first customer. However,if charging were denied due to capacity issues, the PEV would, forexample, be punished thus moving it to a lower state (e.g., p₂=0.25) andthereby reducing its request rate. This approach will result inless-urgent customers having a lower overall probability of completingcharge than more-urgent customers. That being said, for the same amountof charge, the less-urgent customer pays a lower price.

In such approaches, the customer has control over what price they arewilling to pay to meet their charging needs. To implement theseapproaches, the charge manager will simply need to determine and presentto all customers either a price-per-packet or a price-per-request rate.Based on price thresholds established by the customer, an automaton canbe developed (locally, i.e., anonymously) that reflects their urgency tocharge. That is, the request probability will increase with urgency andwill be reflected by increasing the values loaded in the automaton'sstates (i.e., p in FIG. 14).

More generally described, some embodiments of a probabilistic automatonimplement the Gur game. A probabilistic N-state automaton illustratesthe ability to control participation for a larger range of nodes andwith improved fairness of participation among nodes. For PEV charging,this latter automaton design was leveraged, of which a simple version(N=3) is presented in FIG. 7.

As shown in the state diagram (FIG. 7), if the node (PEV) is in itsmiddle state, it will transmit during a particular epoch (time period)with probability P₂. In the PEV application, this “transmission”corresponds to the PEV requesting a packet of charge for a finite lengthof time (or epoch). If the request can be supported by theinfrastructure, the vehicle is allowed to charge for one epoch. With asuccessful request, the state machine moves to the next higherprobability state P₁ and transmit during the next epoch with probabilityP₁>P₂. If the request is not successful, the PEV would not charge forthe epoch, would move to the next lower probability state P₃, and wouldrequest at the next epoch with probability P₃<P₂. This automatonapproach has been shown to adapt to scenarios where the distributioncapacity varies over time.

For fair and consistent treatment across all PEVs, each user's automatonwould be of the same design. However, in order to ensure that driverswho need to charge their vehicles more quickly are able to do so, thedesign can be adjusted to give such vehicles a higher priority. ‘Urgent’users willing to pay for preferential charge allocation can beaccommodated, for example, with a different automaton design havinghigher state probabilities than that for ‘non-urgent’ customers or withan automaton (as illustrated in FIG. 7) where ‘urgent’ users may requestcharge at each epoch.

Packetization of PEV Charge

Why is PEV home charging a candidate for packetized delivery? Firstly, a5-8 kW AC Level-2 PEV charger is likely to be the highest power load ina home; if many chargers in a neighborhood were to run simultaneously,substantial infrastructure degradation could result, particularly inolder distribution systems. However, most PEV owners with Level-2chargers will not need to charge their vehicles immediately upon vehiclearrival at home. Given fast charge rates, there is likely to be morethan sufficient time overnight to bring a PEV's battery to the desiredstate of charge (“SOC”) for the next day's driving. In short, it istypically not necessary that PEV charging be continuous from start tofinish.

Packetized charging breaks the required charge time into many smallintervals of charging (i.e., ‘charge-packets’). For example, 4 hours ofLevel-2 charging could be accomplished with 48, 5-minute charge-packets.A PEV (or its charge station, etc.) would request the authorization tocharge for the packets duration. A charge-management coordinator deviceat the distribution substation would assess local conditions anddetermine whether additional load on the system can be accommodated. Ifallowed, the PEV will charge for the duration of the packet and thensubmit new requests for subsequent packets until the battery is fullycharged. If charging cannot be accommodated, the PEV resubmits a requestat a later time.

Other random-access control methods developed for random-access channelsinclude Aloha, Slotted-Aloha and Carrier Sense Multiple Access (CSMA),each of which requires very little (if any) data exchange between thesource and loads in the system. Any random-access control method(s) maybe used with the presently disclosed packetized charge methodology.

Exemplary System-Level Implementation Approaches

Key advantages of the proposed packet-based CM approach are that: (1)the scheme can be used to manage constraints anywhere in a distributionsystem; (2) the communication requirements are minimal; and (3) customerprivacy is maintained. Here these advantages are illustrated bydescribing potential implementation approaches and contexts.

The packetized method and systems can be implemented to mitigateoverloads at multiple locations within a distribution system.Embodiments could be used to avoid over-temperature conditions on, forexample, a medium-voltage distribution transformer, an undergroundcable, a low-voltage service transformer; under-voltage conditions inany of these example locations; or (using a hierarchical design) acombination of such constraints. In each case, the charger automatonwould communicate with an aggregator responsible for managing one ormore particular constraints (e.g., feeder or transformer overloads). Forexample, in the case of medium-voltage system constraints, theaggregator could be located at the distribution substation. For the caseof service-transformer constraints, the aggregator could be located atthe transformer. The only data required to flow from the PEV charger tothe aggregator would be charge-packet requests. The aggregator wouldrespond to requests based on available capacity. In each of these cases,communications would occur over Advanced Metering Infrastructuresystems, which typically have very low communications bandwidth and highlatencies, emphasizing the importance of a scheme that makes limited useof this bandwidth.

It is also possible to implement communications for the packetizedmethods with either one-way (simplex) or two-way (duplex) data flows. Inthe two-way case, the aggregator may respond to each requestindividually with either an approval or denial. In the one-way case, theaggregator may broadcast the state of the resource (either overloaded,or not-overloaded) and chargers would make their request locally byrandomly “listening” to the broadcast signal. The latter version hasadvantages in terms of privacy, as the transformer is blind to who isreceiving permission to charge.

Combinations of these schemes could be employed simultaneously. That is,a PEV charger might only send requests to an aggregator at thesubstation, if a service transformer's broadcast signal indicated thatthere was local capacity available. In other examples, automatons forPEVs may have a first scheme, while automatons for air conditioners mayhave a second scheme (which may be different than the first scheme).

EXAMPLES

The following example sets are intended to be non-limiting and used forthe purpose to further describe the techniques of the presentdisclosure. It should be recognized that other automaton designs may beused, more than one automaton design may be used, and otherimplementations of charge management systems using packetized chargesare all within the scope of the present disclosure.

Example Set 1—2-State Automaton

To illustrate the proposed method, a simple and readily scalable exampleis presented in which the charging of 100 PEVs needs to be managed. Inthis set of examples, Level-1 home charging for the vehicles is assumed,and it is assumed 10 hours (i.e., 120, 5-minute power packets) isrequired for a vehicle to complete a full charge (0-100%). Threeexamples (1A, 1B, and 1C) are considered to illustrate the flexibilityand robustness of the approach rather than to provide specificperformance numbers. Table 1 summarizes the simulation constraints forexample set 1. For each of these examples, a normal distribution ofevening times when the PEV charging can start and when it can end wasassumed, corresponding to PEV home arrival and departure times. For eachPEV, a vehicle plug-in/plug-out time was established to determine thewindow of charging opportunity (see FIG. 2).

TABLE 1 Simulation Parameters for Example Set 1 Parameter Distributionplug-in time normally distributed between 1700 and 1900 hours plug-outtime normally distributed between 0600 and 0800 hours power packet 5minutes duration charge time required Example 1A & 1B - All vehicles 10hours (i.e., 120 ‘packets’) Example 1C - Uniformly distributed between 5and 10 hours

Example 1A: Fixed Demand, Variable Supply

Example 1A is illustrative of a “worst-case scenario” where all 100 PEVsrequire the maximum 10 hours of charging during the evening (i.e., eachPEV requires 120, 5-minute power packets). In this example, the simpleN=2 state automaton of FIG. 1 was set to have P₁=1.0 and P₂=0.5 for all100 PEVs.

FIGS. 3A-3C show the ability of automaton-based random access approachof this example to fulfill the charging requests of 100 PEVs when thepower system has variable capacity. In FIG. 3A, it can be seen thatunder the conditions where the supply is variable (solid line—50, 80,100, 90, and 50 PEVs), the automaton approach allows the PEVs in anuncoordinated manner to utilize the capacity (dashed line) nearlycompletely. One will note some latency as the capacity changes from 80to 100 PEVs. This is a result of many PEVs being in their lowerprobability state (as the capacity was previously constrained) and thusnot requesting permission to charge in the same epoch. FIG. 3B shows thecharge activity (white spaces) of each PEV (by PEV ID along the y-axis)over time (x-axis) of the 100 PEVs being considered.

Note that from 1700 hours to 1900 hours we see the effect of thedistributed plug-in times. We also note a great deal of ‘packetization’in the charging due to the system only being able to handle 50 PEVsinitially. As capacity increases, PEVs are able to charge on a moreconsistent basis. At full capacity (2300 to 0200 hours) all PEVs areable to charge continuously. Competition for and sharing of chargingresources is reinstated when capacity drops at 0200 hours and then againat 0500 hours, resulting in increased turnover in the use of theavailable capacity.

The automaton rewards and punishments are communicated by the chargemanager based on system capacity and do not take in account which PEV ismaking the request. A measurement of effectiveness is whether thisapproach will result in all PEVs receiving their requisite charge. FIG.3C shows the resulting charge distribution by PEV ID. Overall, Example1A had 1110 PEV·charge-hours available over the 15-hour window from 1700hours to 0800 hours, of which an average PEV was plugged in for only 13hours (FIG. 2). Using the random access approach (again, with no apriori scheduling) the presently disclosed method was able to achieve994.25 PEV·charge-hours of the 1000 PEV·charge-hours requested (i.e.,99.425% success in meeting demand). For this example, most PEVs wereable to charge fully and the worst-case charge for a PEV was >88% (forPEV ID=35).

By increasing the number of states and choosing the probabilities ofeach appropriately, latency in response can be drastically reduced. Inshort, a ‘better’ automaton would be expected to decrease the notedlatencies and to further increase this efficiency.

Example 1B: Fixed Demand, Insufficient Supply

In Example 1B, the capacity profile of FIG. 3A was utilized and the(supply) capacity was reduced across the board by 75% and then to 50%.That is, the overall capacity during the charging window is reduced from1100 PEV·charge-hours to 832.5 PEV·charge-hours, then to 555,respectively. As such, neither of these cases are capable of meeting thefixed demand of 1000 PEV·charge-hours.

For the 75% case, 787.16 PEV·charge-hours were completed out the totalof 832.5 available in the 15-hour window for a 94.55% utilization rate.For the 50% case, 527.41 PEV·charge-hours were completed out the totalof 555 available in the 15-hour window for a 95.03% utilization rate.FIG. 4 shows that: (1) the automaton-based, random access approach toPEV charge management results in all users being impacted in a‘democratic’ manner; and (2) the simplistic, uncoordinated approachstill achieves good utilization of the available resources. Example set2 (below) shows that variability from one user to the next can befurther reduced with an automaton having more than just N=2 states.

Example 1C: Variable Demand, Variable Supply

In Example 1C, a more realistic case was considered where the 100vehicles have variable charge needs uniformly distributed from 5 to 10hours (i.e., 50% and 100% charge, respectively). For this case, eachPEV's automaton is unique not in structure (all PEVs employ a 2-stateautomaton), but in the probabilities assigned to each state. Theprobability for the highest state (P₂) was chosen to be simply thepercentage of charge needed (see FIG. 5). The lower state probability(P₁) was set to half this value.

The same capacity profile as Example 1A and 1B was used. FIG. 6A showsthe charging capacity and utilization over the 15-hour charging window.As the overall demand (775.4 PEV·charge-hours) is less than thecapacity, there are times where not all PEVs are chargingsimultaneously. That is, with the random access approach where many PEVshave low needs, the charging activity becomes broadly distributed overthe available window. This is more clearly shown in FIG. 6B where thePEVs with greatest need (smaller ID numbers) have more consistent chargeactivity than PEVs with lesser needs (larger ID numbers), especially asthe capacity increases. Finally, as shown in FIG. 6C, each vehicle fullycompletes its required charge over the 15-hour window.

Example Set 2—3- and 4-State Automatons

To illustrate embodiments of the present method accounting for urgency,simple and readily-scalable examples (2A, 2B, and 2C) are provided inwhich the charging of 100 PEVs needs to be managed. For the examples ofthis set, it is assumed that system uses Level-1 home charging, and thateach vehicle will achieve a full charge (0-100%) in 10 hours (i.e., 120,5-minute power packets). Table 2 summarizes our simulation parametersfor this set. For each of these examples we assume each PEV can receivea full 10-hour charge.

The first two cases consider the same supply profile (FIG. 15) thatinitially accommodates all vehicles but becomes increasingly limited. Toillustrate the approach we assume that 100 PEVs are connected to afeeder that has variable amount of power that can be allocated forcharging (up to 192 kW).

TABLE 2 Simulation Parameters for Example Set 2 Parameter Value Chargeneed 10 hours (full charge - Level 1) per PEV Power packet 5 minutesduration Example 2A All PEVs at urgency 1.0; charge window 10 hoursExample 2B PEV urgency evenly distributed between 0.2, 0.4, 0.6, 0.8 and1.0; charge window of 10 hours. Example 2C Urgency profile of Example2B; charge window is extended to 12.5 hours providing additionalcapacity

There is a constant demand of 12,000 (120 charge intervals/PEV×100 PEVs)power packets in these cases but, with a charge window of only 10 hours,the overall the capacity is 80% of that need (i.e., 9,600 powerpackets). For the last example of this set, the profile is similar butthe overall window length is 12.5 hours resulting in a full 12,000 powerpackets being available. The objectives of the management scheme are to:(1) provide priority charging for those customers willing to pay theupcharge; and (2) ensure all the system capacity is indeed used even ifcustomers are stating low urgency.

Example 2A: Fixed Urgency, Variable Capacity

For Example 2A, a scenario was simulated where all 100 PEVs require themaximum 10 hours (i.e., each PEV requires 120, 5-minute power packets)and all users have maximum urgency (i.e., p=1 in FIG. 14). Clearly thiscase will not accommodate all users fully. In fact, if the chargemanager was ideally fair, it would not accommodate any customer fully.FIGS. 16A-16B illustrate the random access approach achieved throughusing the proposed approach. The system can initially serve all PEVs(“charging” indicated in white). As the feeder becomes constrained, allPEVs have reduced and random access to charging. Black indicates “notcharging”. As illustrated, on average each PEV receives 80% of itsrequired charge and the system's capacity, albeit constrained, is fullyutilized.

Example 2B: Variable Urgency, Variable Capacity

In Example 2B, a scenario was simulated where different users assigndifferent urgency to the day's charging. A low-urgency customer iswilling to pay only the lowest rate for the received power and as aresult the customer is willing to take less than a full charge. Incontrast, the highest-urgency customer is always willing to take acharge regardless of price. This dichotomy was implemented through theautomaton shown in FIG. 17 using the parameters presented in Table 3.Using the previous capacity profile (FIG. 15), the automaton approachindeed meets the objectives. Most urgent customers receive a powerpacket nearly every epoch to fully meet their need. Less urgentcustomers (ID>20) share the capacity. Specifically, it can be seen (bythe white band at the top of FIGS. 18A-18B) that those PEVs (ID No.1-20) with highest urgency (p=1) nearly all receive full charge. Throughthe completely uncoordinated accessing of the power distribution system,the approach manages to proportionally allocate the capacity by urgencyas illustrated in Table 3.

TABLE 3 Additional Simulation Parameters for Example Set 2 Power packetsMean % PEV ID Urgency received completed Deviation %  1-20 p = 1.0118-120 99.5% 0.6% 21-40 p = 0.8  88-104 81.5% 3.6% 31-60 p = 0.6 67-7458.1% 3.0% 61-80 p = 0.4 38-57 40.6% 4.7%  81-100 p = 0.2 17-29 19.7%3.2%

While the automaton used in Example 2B (FIG. 17) achieves the expectedresults, it has the downside of not effectively utilizing the availablecapacity in the system. As many PEVs were set to have low urgency (e.g.,0.2 or 0.4) the frequency of their charge requests were such that theoverall utilization of the available capacity was only ˜60% in thisexperiment. As such, an alternative automaton that provides bothpriority and more effective resource utilization was simulated inExample 2C (below).

Example 2C: Variable Urgency, Sufficient Capacity

In Example 2C, a more realistic case was simulated where there issufficient capacity in the system but there is a desire to prioritizethe charging among users (again, by a customer's willingness to pay forthat level of service). The automaton of Example 2B enabled priority butnot the efficient use of the capacity. In Example 2C, even thelowest-urgency users were allowed to achieve a state where they willrequest a charge during an epoch with certainty (FIG. 19). Allowinglow-urgency customers the ability to reach a p=1 state improves overallutilization of the distribution system capacity.

The experiment of the previous example was repeated with the chargewindow increased to 12.5 hours. This provides a capacity equal to thefull PEV demand (i.e., 12,000 power packets). The results are seen inFIGS. 20A-20B.

Ideally, PEVs No. 1-20 would charge continuously for the first 10 hours(as they have the highest urgency) and then the remainder of the PEVscomplete their charge in order of remaining urgency (i.e., 0.8 to 0.2).However, that would require coordination between the charge manager andthe individual PEV chargers that, due to privacy and securityconsiderations, was not desirable. FIG. 20A shows that all high-urgencyPEVs complete their charge in about 11 hours. Furthermore, all PEVs withurgency greater than 0.6 receive effectively a full 10 hours of charging(FIG. 20B). Only the lowest-urgency PEVs do not complete full chargingeven though there was capacity (were the capacity to be ideallymanaged). Overall in this experiment, the capacity was 96.2% utilized(again, without any specific coordination by the charge manager, uniqueidentification of individual customers, etc.)

Example Set 3—Comparison Charge Management Schemes Example 3A: A ServiceTransformer Using Charge-Packet CM

For illustrative purposes, the charge-packet method is applied to thecase of a constrained, low-voltage service transformer. In this example,a 30 kVA transformer serves 20 homes and 10 PEVs. The baselineresidential load patterns were scaled to an average of 1 kVA per home(with a 0.9 power factor). The PEV travel patterns were randomly sampledfrom the New England travel survey data of the National Household TravelSurvey (“NHTS”) from the U.S. Dept. Transportation, Federal HighwayAdministration (2009). Each vehicle was assumed to charge using ACLevel-2 charging rates (7 kW at 1.0 power factor). The electric vehiclecharacteristics roughly reflect those of the GM Volt. The travelefficiency is 4.46 km/kWh in electric mode, and 15.7 km/L in gasolinemode, with a 13 kWh usable battery capacity. While all of the simulationresults in this example are for series Plug-in Hybrid Electric Vehicles(PHEV), the packetized method could just as easily be applied to purebattery electric vehicles (BEV). However, for the BEV case, the travelsurvey data are likely to be a less accurate representation of travelbehavior, since BEV drivers may adjust their travel patterns given thereduced range of the vehicle. For this reason, PHEVs were selected forthe simulation rather than BEVs.

For the charge-packet CM method, it was assumed that drivers can decideto choose the urgent mode, and that once chosen, this choice is constantduring the day (the simulation duration). In the urgent mode, thevehicle requests charge regardless of the price of electricity, and itsautomaton stays at P₁ (the highest probability). In the non-urgent mode,the vehicle requests charge only during off-peak hours, and itsautomaton can go to lower states in case of charge denial.

For Example 3A, the following assumptions were used: (1) all PEVs werein the non-urgent charging mode (off-peak hours assumed to be from 8p.m. to 8 a.m. the next day); (2) each PEV charger was managed with athree-state (N=3) automaton as illustrated in FIG. 7 (with requestprobabilities of P₁=1, P₂=0.5 and P₃=0.25); and (3) time epochs were setto 15 minutes.

FIGS. 8A-8C show the results of this simulation. FIG. 8A shows thetransformer load with and without PEV charging. While the loadapproaches the 30 kVA limit, the constraint is satisfied over the entireperiod. FIG. 8B shows the status of each PEV status over the day, withwhite bands showing the randomly scattered 15-minute periods, duringwhich each vehicle was charging. FIG. 8C shows the how the automatonstates change during the day. During off-peak hours, the automatons aremore likely to sit in the lower state (P₃). Recall that these states aredetermined locally, based only on whether the vehicle is permitted tocharge after its most recent request. Despite the fact that there is nocommunication between the vehicles, the automaton states show a highcorrelation during each epoch.

Previous CM Schemes

The results in FIGS. 8A-8C illustrate that the decentralizedcharge-packet CM approach can be used to keep PEV loads below a desiredlimit. Examples 3B and 3C describe two comparison schemes that were usedto evaluate the relative merits of the charge-packet approach of thepresent disclosure.

Example 3B: Simple First-Come, First-Served Charge Management

A simpler, decentralized approach to the CM problem would be to allowany vehicle to charge, and to continue to charge, so long as there wascapacity available. Like the charge-packet method, this approach isdecentralized and can be implemented with very limited communications.In the simulated implementation of this concept, PEVs are allowed tobegin charging as soon as they arrive at home during both peak andoff-peak hours, unless there is insufficient capacity in thetransformer. Once charging begins, it continues until one of thefollowing occurs: the battery is fully charged, the PEV leaves home, orthe transformer becomes overloaded by an increase in non-PEV load. Inthe latter case, the transformer randomly chooses a vehicle to stopcharging.

FIGS. 9A-9B illustrate results from this approach for the same10-vehicle scenario as in Example 3A. In this case, vehicles have morecontinuous charging patterns (as seen by the continuity in the whitebands in FIG. 9B). Because time-of-use prices are not considered byPHEVs in this method, they charge regardless of the time of day, as longas the transformer is not overloaded. In this case, vehicles that arrivelater in the day or are initially denied charge are at a disadvantagebecause they cannot start charging until there is sufficient capacity tosupport additional PHEV charging. As a result PHEVs 9 and 10 do notstart charging until the early hours of the morning (FIG. 9B). Incontrast, the randomized nature of the packetized approach solves thisfairness problem by requiring vehicles to request new packets at eachepoch, providing vehicles with equal access to the resource, regardlessof arrival times. In the packetized simulation (Example 3A), vehicles 9and 10 charge during several intervals during the night, with the firstpackets shortly after vehicle arrival. In FIGS. 9A-9B, PHEVs 9 and 10 donot get any charge until after 1 and 2 am respectively. The extent towhich vehicles get equal access to charging is quantified and comparedbelow (see FIG. 13).

The FCFS charging scheme is a useful comparison scheme for two reasons.First, it illustrates how much charging costs increase, if PHEVs are notresponsive to time-of-use prices, having the same travel pattern as inpacketized charging method. Second, the FCFS method illustrates thepotential of the packetized approach to provide equal access toconstrained resources for all PHEVs.

Example 3C: Optimal Charge Management

The second comparison method is a centralized, optimal CM scheme. Theoptimization method was used to identify the minimum cost chargescenario. In order to ensure that every vehicle traveled their totaldemand in the survey data, and estimate daily travel costs under eachcharging scheme, all vehicles were assumed to be serial plug-in hybridelectric vehicles, with gasoline used after the usable battery capacitywas expended.

The optimization problem is a mixed integer linear programming model.Only the objective function and modifications to the model are describedhere.

The objective in the optimization method is to minimize the retail coststo vehicle owners associated with traveling the miles described in thetravel survey data. Because the vehicles are PHEVs, and the homes arecharged for electricity using time-of-using pricing, there are threefuels that can be used for charging: on peak electricity, off peakelectricity, or gasoline. The resulting objective (cost) function isgiven in (1):

$\begin{matrix}{C_{t} = {\sum\limits_{t = 1}^{T}\;{\sum\limits_{v = 1}^{N}\;\left\lbrack {\frac{{\pi_{e}(t)} \cdot {P\left( {v,t} \right)} \cdot h}{\eta_{e}} + \frac{\pi_{g} \cdot {d_{CS}\left( {v,t} \right)}}{\eta_{g}}} \right\rbrack}}} & (1)\end{matrix}$

where π_(e)(t) and P(v,t) are the price of electricity and the chargingpower of battery of vehicle v at time t, h is the charge epoch length,η_(e) is the overall efficiency of the charging system (η_(e)=0.85),π_(g)=1.06 $/L is the price of gasoline, d_(CS)(v,t) is the distancetraveled after the battery was depleted (charge-sustaining (“CS”) mode),η_(g)=15.7 km/L is the CS mode vehicle efficiency, and T and N are thenumber of epochs and vehicles, respectively. In the present example,one-hour epochs were used (h=1), and P(v,t) was a continuous variablethat varied between 0 and 7 kWh. In order to obtain consistent results,the following two constraints were added to previous models:

$\begin{matrix}{{{{{\sum\limits_{v = 1}^{N}\;{P\left( {v,t} \right)}} + {P_{r}(t)}} \leq {\overset{\_}{P}\mspace{14mu}{\forall t}}} = 1},\ldots\mspace{14mu},T} & (2) \\{{{{P\left( {v,t} \right)} \leq {{P\left( {v,{t - 1}} \right)}\mspace{14mu}{\forall v}}},{t\text{:}}}{{d_{tot}\left( {v,t} \right)} = {{d_{tot}\left( {v,{t - 1}} \right)} = {{{0\&}{\pi_{e}(t)}} = {\pi_{e}\left( {t - 1} \right)}}}}} & (3)\end{matrix}$

where P_(r)(t) is the total residential load at time t, P is the loadlimit for the transformer or feeder, and d_(tot)(v,t) is the totaldistance traveled by vehicle v at time t. Constraint (2) ensures thatthe transformer is not overloaded, and (3) forces PHEVs to charge assoon as possible, so long as the total cost is not affected. In otherwords, if the total distance traveled by PHEV v is zero in twoconsecutive time slots (if the PHEV is plugged in at home and the priceof electricity is the same at time t and t−1), the charging power ofvehicle v's battery should be greater at the earlier time slot.

FIGS. 10A-10B show results for this optimal charging scheme for the10-PEV case considered in Examples 3A and 3B. As a result of allowingvehicles to charge at any rate, the approach chooses charge rates thatare lower than the full Level 2 rate. This type of “Unidirectional V2G”has advantages in terms of more refined control, but requires additionalcommunication and coordination. As expected, optimal CM fully utilizesthe transformer capacity during off-peak hours, but only if travel plansare fully known. The other two methods also keep loads below the powerlimit, but with somewhat more variability.

Example Set 4—Further Comparisons of the Methods of Example Set 3

In this example set, simulation results are described for a larger casein which a 500 kVA medium voltage transformer is serving 320 homes with1 kVA average load. Each home has two vehicles (i.e., 640 vehicles intotal), either or both of which could be a PHEV depending on the PHEVpenetration level. The number of homes was selected such that the peakresidential load was below the transformer's rated load. It was assumedthat customers were charged for electricity according to a two-rate,time-of-use residential tariff in which the peak (8 a.m. to 8 p.m.)electricity rate is π_(e)(t)=$0.14/kWh and the off-peak rate isπ_(e)(t)=$0.10/kWh. These assumed values are representative of (thoughless extreme than) current retail time-of-use rates in the NortheasternUS. For the packetized case, it was assumed that vehicles in urgentcharging mode were charged the peak price ($0.14/kWh) during peak hours.This $0.04 difference between urgent and non-urgent rates is likelyconservative, since the cost to utilities of providing non-urgentcharging is likely to be only slightly higher than off-peak wholesaleenergy costs, which are frequently $0.02-$0.03/kWh in the NortheasternUS.

In order to obtain a distribution of outcomes over a variety of likelytravel patterns, 100 unique vehicle travel patterns were randomlyselected from the survey data.

Comparing packetized charging to optimal and FCFS charge management

A two-state automaton was modeled for the charge-packet method, withrequest probabilities of P₁=1 and P₂=0.5. Furthermore, vehicles were setto urgent mode (for the packetized approach) based on the solution fromthe optimization: if PHEV v charged during peak hours in theoptimization results, v was set to urgent charging mode. Essentiallythis reflects the assumption that drivers were able to estimate theirneed for urgent charging.

Three different levels of PHEV penetration: 12.5% (N=80), 25% (N=160)and 50% (N=320) were simulated. Note that these high penetration levelsare relatively unlikely in the near term for the aggregate vehicle-fleetin most countries. However, it is not unlikely that some residentialneighborhoods could have PEV penetrations that are substantially higherthan that of aggregate. As a result of this, and the fact that temporalpatterns in non-residential loads differ from residential patterns, weassume that the simulated PHEVs do not impact the two-tier time-of-useprice. Also, it was assumed that the aggregate system load curve, whichwould include commercial and industrial customers, is different from theresidential load shown in FIG. 11, which shows the baseline and totalload for 25% PHEV penetration (160 PHEVs) for each CM scheme. In orderto make a clear comparison, 1-hour time slots for the FCFS andoptimization method were chosen, as well as 1-hour request intervals andpacket lengths (i.e., epochs) for the charge-packet method. FIG. 11shows that the PHEVs in the charge-packet case use slightly more peakhour charging, than in the optimization case, which increases theoverall costs for the charge-packet method somewhat. However, thepresumption is the unrealistic requirement that the central optimizationapproach can obtain perfect information about travel plans. What isnotable is that the charge-packet scheme keeps loads below the limit,with costs that are nearly optimal as the load presented to the systemis adjusted over time and distributed across PEVs in the system.

The average total travel cost per PHEV over 100 one-day Monte Carlosimulations was compared. Each vehicle was assigned a random travelpattern from the survey data. The same vehicle-travel patterncombinations were used identically for each scenario, to ensure a faircomparison. The results for two different PEV penetrations (12.5% and50%), and two different battery capacities are shown in FIGS. 12A-12D.The gasoline, off-peak and on-peak electricity costs are shownseparately. FIGS. 12A-12D show that the total travel cost of thecharge-packet method is slightly more than that of the optimizationmethod, but much less than the simple method. The charge-packet costsare slightly greater because urgency settings were constant during theday, based on the realistic assumption that drivers are not perfectoptimizers. The simple method is more costly because in this casedrivers do not differentiate their charging based on the price ofelectricity. The result is that in the simple method, vehicles consumemore peak-hour electricity than in the other methods. One exception isthe case of 50% penetration and 24 kWh batteries, where all chargingmethods use the entire transformer capacity during off-peak hours, butthe optimization method can optimally allocate charging to those PEVsthat cannot get peak-hour charging. In other charging methods, some PEVsthat are not capable of receiving peak electricity (because of not beinghome) do not get enough charge overnight, and must use the mostexpensive fuel, gasoline. It should be noted that in the simulations,peak electricity is still cheaper than gasoline in terms of $/km travel.

Generally, in the higher PEV penetration scenarios, there wasinsufficient off-peak electricity to allow all vehicles to fully chargetheir batteries, resulting in more peak electricity usage for theoptimization and packetized scenarios. Because of this, increased PEVpenetrations resulted in a slight increase in travel costs for theoptimization and packetized cases. For these two charging methods, inthe 12.5% PEV penetration case vehicles can use more off-peakelectricity than in the 50% PEV penetration case, where peak electricityis used more.

As one would expect, the results indicate that larger battery capacitiesresult in reduced use of the most expensive fuel, gasoline, and thusreduce travel costs. However, the impact of the larger batteries isdifferent in low and high PEV penetration cases. In the low penetrationcase, more off-peak electricity can be used for the larger battery asmore transformer capacity is available; in the high penetration case,the transformer capacity is exhausted for both the 13 kWh and 24 kWhbattery cases during the off-peak hours, making the benefits of largerbatteries less clear.

Most importantly, these results show that the cost of using thepacketized method is only 0.9% to 5.2% greater than what was found forthe optimal CM case (as opposed to 3.1% to 14.1% for the simple CMscheme). The charge-packet method requires much less information fromthe PEV owner (only the choice of an urgency setting) and requires farless two-way communication than would be required to implementcentralized optimization method. In summary, it was found that thecharge-packet method can achieve near optimal costs, while preservingdriver privacy and being robust to random changes in travel behavior.

Example Set 5—Comparing Variants of the Charge-Packet Method

The state machine used in the packetized PEV charger allows PEV chargingto adapt to reduce the impact on the distribution system, such asoverloaded transformers or feeders. However, different state machineprobabilities will change the performance of the charge-packet method,particularly with respect to the burden on the communicationsinfrastructure. To investigate the performance of the charge-packetmethod, the idea of differentiating between charge-packet lengths (i.e.,the time epoch a PEV is given permission to charge) and requestintervals (i.e., the time epoch between two requests for charge) wasexplored

The charge-packet method was simulated with different state-machineprobabilities, packet lengths (5-minute and one-hour), and requestintervals (5-minute and one-hour). The results were compared acrossthree metrics: (1) average total cost; (2) a measure of the extent towhich the method provided each vehicle with equal access to the chargingresources; and (3) the number of messages transmitted by the PEVs or thetransformer, per vehicle-day, in the bi-directional (duplex)communication case.

One of the problems observed with the FCFS charging case (Example 3B)was that vehicles that began charging earlier than others, before aperiod in which charge mitigation occurred (typically early eveninghours), were not required to stop charging when new vehicles arrived. Asa result, vehicles that arrived later in the day frequently were notallowed to begin charging until capacity in the system was released,effectively giving them “less equal” access to charging resources. Inorder to measure the extent to which vehicles were given equal access togrid resources under different scenarios, an Equal Access Metric (EAM)was defined to assess the “fairness” of each method. For this purpose,the probability of charge mitigation was found for each vehicle v, P_(M)(v), by dividing the number of time slots that the PEV charge request isdenied by total number of time slots that the PEV is requesting chargefrom the transformer. P_(M) was computed only for off-peak hours, whenall vehicles, whether in urgent or non-urgent mode, were requestingcharge. Given the standard deviation of P_(M) (v) over all v, σ(P_(M)),EAM was calculated as follows:EAM=1−σ(P _(M)).  (4)

σ(P_(M)) ranges between 0 and 1, which means that EAM has the samerange. Therefore, a method with perfectly equal access will have EAM=1,and lower values of EAM indicate that some vehicles are given moreaccess than others. The rationale for this metric is that as long as allthe PEVs are mitigated with the same probability (i.e., the same ratioof mitigation to total requests) the method maintains its fairness.

Communication burden was measured by counting the number of messagesexchanged over the communications network per vehicle per day. Followingthe two-way communication system design, each charge packet request wasassumed to require one message submission to the aggregator. If the PEVreceives a reply (one message), this means that the request is approved,otherwise the charge request is denied.

FIG. 13 shows these three metrics, for three different chargetime-interval combinations and four different state machines, along withresults for the simple charging method. Time-interval combinations aredefined using the notation t₁/t₂, in which t₁ is the interval of timesbetween requests and t₂ is the length of the charge packet, both inminutes. The three time-interval combinations compared were 60/60, 5/60and 5/5, and the state machines were SM₁: {P₁=1, P₂=0.5}, SM₂: {P₁=1,P₂=0.5, P₃=0.25}, SM₃: {P₁=0.8, P₂=0.4} and SM₄: {P₁=0.8, P₂=0.4,P₃=0.2}. As expected, smaller request intervals and charge-packetlengths reduced charging costs, but increased communication costs. The5/60 gives about the same travel cost as 5/5, but at the expense offairness (reduced EAM). It is possible that excessively frequent on/offcycles could have adverse effects on the battery or charging systems. Ifthis was the case, the 5/60 method could be preferable, given that theincrease in cost is negligible. Note that 5/60 outperforms 60/60 interms of equal access.

The results also suggest that using state-machines with N=3 rather thanN=2 states, or with lower transition probabilities, can substantiallyreduce the burden of CM on the communications system. However, thesechanges also result in small increases in travel costs. Ifcommunications bandwidth is not a constraint, the 5/5 charge-packet issuperior (of those simulated) in terms of both total cost and equalaccess.

Example Set 6

An aggregator for providing power to one or more nodes is described. Theaggregator comprises a source interface in electrical communication withan electrical power source, and a load interface in communication withthe one or more nodes. The aggregator is configured to receive requests,from the one or more nodes, for power packets of electrical power, thepower packets configured as electrical power for a finite duration. Theaggregator is configured to determine whether to grant or deny eachrequest based on the availability of electrical power from theelectrical power source, and provide a power packet to each nodeaccording to the corresponding request determination.

A node for requesting electrical power from an aggregator comprises anaggregator interface in electrical communication with the aggregator,and a state register for recording a node state. The node is configuredto retrieve a node state from the state register, to determine, based ona request probability, whether or not to request a power packet having afinite duration, for a time interval, wherein the request probabilitycorresponds to the retrieved node state, and request a power packet fromthe aggregator according to the request determination. The node isfurther configured to receive a response to the request, and change thenode state recorded in the state register based upon the receivedresponse. The node is configured to request a power packet by receivinga broadcast state from an aggregator.

Although the present disclosure has been described with respect to oneor more particular embodiments, it will be understood that otherembodiments of the present disclosure may be made without departing fromthe spirit and scope of the present disclosure. Hence, the presentdisclosure is deemed limited only by the appended claims and thereasonable interpretation thereof.

What is claimed is:
 1. A system for providing electrical power,comprising: an aggregator in electrical communication with an electricalpower source, the aggregator configured to authorize the provision ofelectrical power from the electrical power source as a plurality ofdiscrete power packets; and one or more nodes in communication with theaggregator, each node configured to make successive requests for thepower packets, each successive request occurring during a correspondingrespective time interval, wherein each node is configured toindependently determine whether to make a request during a given timeinternal according to a request probability, the request probabilitybeing a probability the node will make a request during one of the timeintervals.
 2. The system of claim 1, wherein the aggregator isconfigured to: receive requests from the one or more nodes; determinewhether to grant or deny each request based on the availability of theelectrical power; and authorize the provision of a power packet for eachnode according to the corresponding request determination.
 3. The systemof claim 1, wherein the aggregator is configured to broadcast a status,and the one or more nodes are authorized to accept a power packet byreceiving an affirmative aggregator status broadcast.
 4. The system ofclaim 3, wherein the one or more nodes are configured to obtain poweraccording to the received aggregator broadcast status.
 5. The system ofclaim 1, wherein each of the one or more nodes has a first state and asecond state, the first state having a first request probability, P₁,and the second state having a second request probability, P₂, whereinthe second request probability is a probability that a node in thesecond state will make a request during the time interval.
 6. The systemof claim 5, wherein the first request probability, P₁, is greater thanthe second request probability, P₂.
 7. The system of claim 6, whereineach of the one or more nodes in the second state is configured tochange from the second state to the first state based upon a grantedrequest.
 8. The system of claim 6, wherein each of the one or more nodesin the first state is configured to remain in the first state based on agranted request.
 9. The system of claim 6, wherein each of the one ormore nodes in the second state is configured to remain in the secondstate based on a denied request.
 10. The system of claim 6, wherein eachof the one or more nodes in the first state is configured to change fromthe first state to the second state based on a denied request.
 11. Thesystem of claim 6, wherein a node of the one or more nodes furthercomprises a third state, the third state having a third requestprobability, P₃, which is lower than the second request probability, P₂,wherein the third request probability is a probability that a node inthe third state will make a request during the time interval.
 12. Thesystem of claim 11, wherein the node having a third state comprises aselector for selecting a power priority.
 13. The system of claim 12,wherein the node having a third state further comprises a sensor, andthe selector is configured to automatically select the power priorityaccording to a signal received from the sensor.
 14. The system of claim1, further comprising a network sensor in communication with theaggregator.
 15. The system of claim 14, wherein the network sensor isconfigured to measure one or more of an ambient temperature, atemperature of a portion of the system, a weather condition, and acurrent load on the electrical power source.
 16. The system of claim 1,further comprising: an upstream aggregator in electrical communicationwith the electrical power source, the upstream aggregator configured toauthorize the provision of electrical power from the electrical powersource as a plurality of upstream power packets, each upstream powerpacket having a finite upstream duration; and at least one additionalaggregator in communication with the upstream aggregator, each of theaggregator and the at least one additional aggregator configured torequest authorization for one of the upstream power packets during anupstream time interval according to an aggregator probability, whereinthe aggregator probability is a probability that the aggregator willmake a request during the upstream time interval.
 17. The system ofclaim 16, wherein the upstream aggregator is configured to: receiverequests from the aggregator and the at least one additional aggregator;determine whether to grant or deny each request based on theavailability of the electrical power source; and authorize the provisionof an upstream power packet for at least one of the aggregator and theat least one additional aggregator according to the correspondingrequest determination.
 18. A method for providing electrical power,comprising the steps of: receiving randomized requests from a pluralityof nodes for power packets of finite duration; determining whether togrant or deny the requests based on the availability of electricalpower; and authorizing the provision of power packets to one or more ofthe nodes based on granted requests; wherein each node is configured asa probabilistic automaton configured to make successive requests for thepower packets, wherein each of the nodes have a plurality of states anda probability a given node will make a request during a given timeinterval changes according to the state of the node.
 19. The method ofclaim 18, further comprising the step of transmitting a response to thenode.
 20. A method for requesting electrical power be transmitted froman electric power distribution network to a node having a processor,comprising the steps of: making, by the node processor, successiverequests for discrete power packets from the electric power distributionnetwork, each successive request occurring during a correspondingrespective time interval, wherein during each of the time intervals, thenode processor independently: determines, according to a requestprobability, whether to request a power packet having a finite duration,the request probability being a probability the node will make a requestduring one of the time intervals; and requests a power packet having afinite duration be transmitted to the node in response to determining,according to the request probability, that a request should be made. 21.The method of claim 20, wherein the step of requesting a power packet isperformed by receiving a broadcast state from an aggregator.
 22. Themethod of claim 20, wherein the step of requesting a power packet isperformed by transmitting a request to an aggregator.
 23. The method ofclaim 22, further comprising the steps of: receiving a response to therequest; and changing the request probability based upon the receivedresponse.
 24. The method of claim 23, wherein the step of changing therequest probability based upon the received response includes: changingto a lower request probability in response to receiving a deniedrequest; and not changing the request probability or increasing therequest probability in response to receiving a granted request.
 25. Themethod of claim 20, further comprising, determining, by the node, therequest probability.
 26. The method of claim 25, wherein the step ofdetermining the request probability includes determining a value of apriority selector, the priority selector indicating a power urgency ofthe node.
 27. The method of claim 26, wherein the value of the priorityselector is set according to at least one of a customer selection and asignal from one or more sensors.
 28. The method of claim 27, wherein theone or more sensors include a node charge level sensor and a nodetemperature sensor.
 29. The method of claim 25, wherein the step ofdetermining the request probability includes determining the requestprobability according to a signal received by a sensor.
 30. The methodof claim 29, wherein the sensor includes at least one of a node chargelevel sensor and a temperature sensor.
 31. The method of claim 20,wherein the node is an electrical load on the electric powerdistribution network.
 32. The method of claim 31, wherein the node is anelectric vehicle charger or a home appliance.
 33. The method of claim20, wherein the electric power distribution network is an alternatingcurrent power distribution network configured to distribute electricpower to a plurality of loads.
 34. The system of claim 1, wherein theelectrical power is alternating current electrical power.